Since all of these numbers have the same variable they can all be added up to get a sum of 10a which is its simplified form.
Answer:
31/4
Step-by-step explanation:
Answer:
lana rhodes
Step-by-step explanation:
Answer:
cubic units
Step-by-step explanation:
We are given that a region bounded by a curves ![x=(y-7)^2](https://tex.z-dn.net/?f=x%3D%28y-7%29%5E2)
x=4 and about y=5
We have to find the value of volume of the resulting solid
To find the volume of resulting solid we are using cylinder method
Substitute the values of x then we get
![(y-7)^2=4](https://tex.z-dn.net/?f=%28y-7%29%5E2%3D4)
![y-7=\pm2](https://tex.z-dn.net/?f=y-7%3D%5Cpm2)
y-7=2 and y-7=-2
y=7+2=9 and y=-2+7=5
Radius of cylinder =r=y-5
and height =h=![4-(y-7)^2=4-y^2-49+14 y=-y^2+14 y -45](https://tex.z-dn.net/?f=4-%28y-7%29%5E2%3D4-y%5E2-49%2B14%20y%3D-y%5E2%2B14%20y%20-45)
Using cylinder method and integrate along y -axis from y=5 to y=9
Volume =![\int_{a}^{b}2\pi r h dy=\int_{5}^{9}2\pi(y-5)(-y^2+14 y -45) dy](https://tex.z-dn.net/?f=%5Cint_%7Ba%7D%5E%7Bb%7D2%5Cpi%20r%20h%20dy%3D%5Cint_%7B5%7D%5E%7B9%7D2%5Cpi%28y-5%29%28-y%5E2%2B14%20y%20-45%29%20dy)
volume=![2\pi\int_{5}^{9}(-y^3+19y^2-115y+225)dy](https://tex.z-dn.net/?f=2%5Cpi%5Cint_%7B5%7D%5E%7B9%7D%28-y%5E3%2B19y%5E2-115y%2B225%29dy)
Volume =![2\pi[-\frac{y^4}{4}+19\frac{y^3}{3}-115\frac{y^2}{2}+225y]^9_5](https://tex.z-dn.net/?f=2%5Cpi%5B-%5Cfrac%7By%5E4%7D%7B4%7D%2B19%5Cfrac%7By%5E3%7D%7B3%7D-115%5Cfrac%7By%5E2%7D%7B2%7D%2B225y%5D%5E9_5)
Volume =![2\pi[-\frac{6561}{4}+\frac{625}{4}+19(\frac{729-125}{3})-115(\frac{81-25}{2})+225(9-5)]](https://tex.z-dn.net/?f=2%5Cpi%5B-%5Cfrac%7B6561%7D%7B4%7D%2B%5Cfrac%7B625%7D%7B4%7D%2B19%28%5Cfrac%7B729-125%7D%7B3%7D%29-115%28%5Cfrac%7B81-25%7D%7B2%7D%29%2B225%289-5%29%5D)
Volume=![2\pi(-1484+\frac{11476}{3}-3220+900)](https://tex.z-dn.net/?f=2%5Cpi%28-1484%2B%5Cfrac%7B11476%7D%7B3%7D-3220%2B900%29)
Volume =![2\pi(\frac{11476}{3}-3804)](https://tex.z-dn.net/?f=2%5Cpi%28%5Cfrac%7B11476%7D%7B3%7D-3804%29)
Volume =![2\pi(\frac{11476-11412}{3})=\frac{128\pi}{3}](https://tex.z-dn.net/?f=2%5Cpi%28%5Cfrac%7B11476-11412%7D%7B3%7D%29%3D%5Cfrac%7B128%5Cpi%7D%7B3%7D)
Hence, volume of resulting solid =
cubic units